On G-S and C-S inverses in *-rings
Janko Marovt, Dijana Mosić · Communications in Algebra · 2024
The notions of the G-S inverse and the C-S inverse are extended from the set of all complex n × n matrices to *-rings. We present new characterizations of these inverses, study their properties, and apply the C-S inverse to introduce two relations on the set R⏧d of all core-EP invertible elements in a *-ring with identity. We explore the connection between these two relations and the star partial order and prove that one of them is a partial order on R⏧d.